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On Randić spectrum of zero divisor graphs of commutative ring $\mathbb{Z}_{n} $ | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 8، دوره 8، شماره 1، خرداد 2023، صفحه 103-113 اصل مقاله (487.63 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2021.27202.1212 | ||
| نویسندگان | ||
| Bilal Rather1؛ Shariefuddin Pirzada* 2؛ Imran Bhat3؛ Tariq Chishti1 | ||
| 1University of Kashmir | ||
| 2Department of Mathematics, Hazratbal | ||
| 3Central University of Kashmir | ||
| چکیده | ||
| For a finite commutative ring $ \mathbb{Z}_{n} $ with identity $ 1\neq 0 $, the zero divisor graph $ \Gamma(\mathbb{Z}_{n}) $ is a simple connected graph having vertex set as the set of non-zero zero divisors, where two vertices $ x $ and $ y $ are adjacent if and only if $ xy=0 $. We find the Randi'c spectrum of the zero divisor graphs $ \Gamma(\mathbb{Z}_{n}) $, for various values of $ n$ and characterize $ n $ for which $ \Gamma(\mathbb{Z}_{n}) $ is Randi'c integral. | ||
| کلیدواژهها | ||
| Randić matrix؛ Randić spectrum؛ zero divisor graph؛ commutative rings | ||
| مراجع | ||
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[13] S. Pirzada, B.A. Rather, T.A. Chishti, and U. Samee, On normalized Laplacian spectrum of zero divisor graphs of commutative ring Zn, Electronic J. Graph Theory Appl. 9 (2021), no. 2, 331–345.
[14] S. Pirzada, B.A. Rather, R.U.l. Shaban, and M.I. Bhat, On distance Laplacian (signless) eigenvalues of commuting graphs of dihedral and dicyclic groups, Springer Proceedings on Algebra and Related Topics with Applications.
[15] S. Pirzada, B.A. Rather, R.U.l. Shaban, and S. Merajuddin, On signless Laplacian spectrum of the zero divisor graphs of the ring Zn, Korean J. Math. 29 (2021), no. 1, 13–24.
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